Questions tagged [instrumental-variable]

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Including Controls for Relevance Test in First Stage Regression of IV?

I am conducting an instrumental variable approach (IV) in my paper, and I am puzzled how to correctly test for the relevance / strength of the instrument assumption. I recently read in a paper by ...
1 vote
1 answer
40 views

What does it mean to "replace all variables with the residuals after projections on any additional exogenous regressors"

I am conducting IV Regression and to make sure that my instrument is not weak, I want to use Montiel Olea & Pflueger (2013) robustness test. (see: Paper by Montiel Olea & Plueger (2013) ). To ...
0 votes
0 answers
32 views

What if the instrumental variable is endogenous in first stage

Suppose $y=\beta_0+\beta_1 x+u,E(xu)\not=0,E(u)=0$. $z$ satisfies $E(zu)=0$ (exogenous) and $Cov(x,u)\not=0$ (relevance). In first stage, we do $x=\pi_0+\pi_1z+v$ and get $\pi_1=\frac{S.Cov(x,v)}{Var(...
3 votes
2 answers
255 views

Some confusions about instrumental variable (econometrics)

As the title says, I have some confusions about instrumental variable. According to my lecture note (which is supposed to be reliable), instrumental variable has two big properties: Validity: an ...
1 vote
1 answer
46 views

Abadie's Kappa (2003) for continuous treatments / IVs

Does somebody know if there exist results and estimators to deal with controls in IV estimation under heterogeneous treatment effects, analogous to Abadie's Kappa (2003) for the binary case? Abadie, ...
0 votes
0 answers
39 views

Errors in variable, statistics/econometrics, measurement error

I didn't understand the deduction involving Plim. Why do the Plim of the terms on the left translate as variance in the first two cases? here is the continuation of the print. were i have the question
5 votes
1 answer
66 views

IV Regression with More Observations for First Stage than Second Stage

This is a very basic question, but I need help. Imagine I have a dataset for variables y, x, and z. I am running an instrumental variable regression such that y is my main outcome variable. So I am ...
2 votes
0 answers
40 views

Examples of instrumental variables for business problems (not rainfall!)

I have been learning about IV as a non-economist and I think I understand the examples I've seen which used rainfall as an IV for modeling the sales of crops or fish at an outdoor market. However, for ...
4 votes
2 answers
86 views

Is my instrument too noisy?

I have an instrument, that I want to use with IV 2SLS, to predict my endogenous variable. The scatter plot of my instrument against my endogenous variable looks like this. Using Stata's binscatter, I ...
1 vote
0 answers
121 views

Instrumental Variable: Bias & larger standard errors

Let's assume the instrument $Z$ satisfies instrumental exogeneity $corr(Z, \epsilon)=0$ and it's relevant $corr(Z, X_{end})≠0$. Where $\epsilon$ is error term and $X_{end}$ is the endogenous ...
1 vote
1 answer
44 views

Using an enrollment probability as an instrument

Can someone walk me through whether this makes sense? Individuals can apply to be enrolled in a treatment (a particular program), or not. The probability of actual enrollment for applicants varies ...
1 vote
1 answer
43 views

IV - Is this correct?

I have the following question. Currently I have an econometric model that uses an instrumental variable, particularly a Bartik instrument (which some people call shift-share). I'm proceding as Mayda ...
1 vote
1 answer
288 views

Can I instrument an endogenous variable and its quadratic form with the instrument and its quadratic form?

I have the following problem, where I would like to have an advise or a reference: I'm estimating a model which usually (in other papers) only includes the explanatory variable in its linear form, but,...
3 votes
0 answers
140 views

How to visualize first-stage in IV regression?

I know what matters is the F-Statistic, but for a presentation it would also be nice to add a plot that visually shows the first stage. How to best visualize that? Say you have an outcome $Y$, ...
1 vote
0 answers
35 views

Adding industry dummies to 2SLS in R

for my Master Thesis I want to regress the ESG score on the stock price drop during the pandemic. For OLS this works fine. To check for potential Endogeneity I also conduct a 2SLS regression with the ...
7 votes
0 answers
146 views

Is 2SLS asymptotically MLE?

$$y_i =\beta_0 +\beta_1 x_{1i}+\beta_2 x_{2i}+\varepsilon_i$$ Suppose $x_1$ is endogenous but $x_2$ is exogenous. We have two excluded instruments, $z_1$ and $z_2$. The first stage is: $$x_{1i} =\...
0 votes
0 answers
45 views

Instrumental Variables - Exogeneity Tests using region characteristics

I am using IV methods to establish the causality, I want to run some exogeniety tests. I have been going over Woolridge (Econometric Analysis of Cross Section and Panel Data, 2010) and I am not ...
1 vote
1 answer
25 views

Estimating parameters when introducing IV Instrument

Say, you have a model $$ y_{it} = \beta_1 a_{it} + \beta_2 b_{it} $$ And you find that $a_{it}$ is endogenous, therefore, you need to find an instrument for it. Say you find an instrument $z_{it} = \...
1 vote
0 answers
35 views

Fuzzy RDD when individuals can affect the probability of treatment

I want to evaluate the effect of getting into a program on earnings. In my case individuals that get a score above $c$ can decide weather to get into the program or not. On the other hand those that ...
3 votes
1 answer
155 views

IV regression: first stage in logs, second stage in levels?

I have a regression in levels, derived from theory. I want to instrument one of the variables, but the best instrument I find has a weak correlation to the endogenous variable in levels, and a strong ...
5 votes
1 answer
63 views

C-statistic when one estimation is just identified

My question is motivated by Do, Joshi, and Stopler's paper "Can Environmental Policy Reduce Infant Mortality? Evidence from the Ganga Pollution Cases". A simplified form of their models that ...
3 votes
0 answers
851 views

Kleibergen Paap F-statistic

I have commonly seen references to a Kleibergen and Paap F-statistic. In their paper, I see a derivation of a chi-squared statistic, but don't see any references to the F-distribution or F-stat. In ...
2 votes
0 answers
288 views

Difference between AR confidence intervals reported in weakiv versus twostepweakiv

Should the Anderson-Rubin confidence intervals reported in weakiv and twostepweakiv be equal to each other? Sun (2018) does not ...
1 vote
1 answer
149 views

IV estimate for entire sample is larger than IV estimates for subsets of sample?

I am using two-stage least squares to estimate a local average treatment effect, with 'treatment' being the endogenous variable and 'assignment to treatment' being the instrument. If I use my full ...
0 votes
0 answers
32 views

Advice on research methodology

I had wanted to ask this community for some advice on some potential methodologies I am developing. Context: I want to evaluate the effectiveness of a component of this scholarship program, which ...
1 vote
1 answer
62 views

Is exogeneity guaranteed for a lottery-generated instrumental variable?

If using $z$ as an instrument for $x$, to study the effect $x$ has on $y$ and given that $z$ was indeed generated through a lottery, is it definite that exogeneity of $z$ will hold? I have looked at ...
4 votes
2 answers
241 views

is endogeneity a problem in the first-stage regression in a two-stage least square regression?

We have this model: $$D=\alpha_1+\gamma_1 Z + \epsilon_1$$ $$Y=\alpha_2+\gamma_2 D + \epsilon_2$$ Notations are as usual: Y is the outcome, D is the treatment, Z is the instrument Two conditions for ...
0 votes
2 answers
102 views

How should I regress income inequality on economic growth?

I would like to know which variables to use to regress income inequality on economic growth. For income inequality, I am thinking of using the Gini index, but don't know what measurement exactly. For ...
2 votes
1 answer
160 views

Interacting covariates with the instrument in the first stage

If I want to run a 2 stage least squares (2SLS) regression with: Relationship of interest: $Y = \alpha + \beta X + \varepsilon $, where $X$ is the endogenous explanatory variable of interest. If I ...
3 votes
1 answer
467 views

Why do we need at least as many instrumental variables as endogenous regressors to identify parameters in 2SLS?

As the title says. Why do we need at least as many instrumental variables as endogenous regressors to identify parameters?
3 votes
0 answers
27 views

Instrumental variable regression: How many interpretations?

I was reading Amemiya "Non-linear regression models" (1983) in which he says that This statement should not be construed as a criticism of Theil's interpretation. I know of at least six ...
0 votes
1 answer
38 views

The instrument in "The Colonial Origins of Comparative Development"

I am hoping to understand when an instrument is appropriate. For the purposes of this question, I'm considering a simplied version of the model in AJR (2000): $$\begin{aligned}\text{GDP} &\sim \...
1 vote
1 answer
237 views

Using dependent variable's and exogenous variables' lags as instruments in 2SLS

Suppose we have the following structural equations: $$y=\beta_0+\beta_1x+\beta_2z_z+\beta_3z_3+\epsilon,$$ where $x$ is the endogenous variable and $z_1,z_2$ are exogenous variables. In the literature,...
2 votes
0 answers
20 views

How to calculate and interpret a marginal treatment effect (local instrumental variable)? (Intuition through simple example.)

I am working on the intuition behind local instrumental variables (LIV), also known as the marginal treatment effect (MTE). I have worked some time on this and would benefit from solving a simple. I ...
2 votes
2 answers
585 views

What does it mean if the controls in my IV model are correlated with my instrument?

I am seeking to understand what it means for my 2SLS IV model if my controls are correlated with my instrument (such that when I add additional controls to my model that are positively correlated with ...
5 votes
1 answer
142 views

Skepticism about the claims of instrument variable validity/exclusion through a statistical test—the Arellano-Bond Test

I am an applied researcher and occasionally come across papers that have panel data and that use dynamic models with both a fixed-effects term and lagged DV (or multiple autoregressive terms): $y_{it} ...
1 vote
0 answers
645 views

Stata's "ivregress 2sls" command - generating F-stats to test for weak instrument

I am transitioning to using the "ivregress 2sls" command in Stata for IV estimates. I've been trying to produce F-statistics to test for whether the instrument is weak. I believe that the ...
11 votes
3 answers
31k views

What is the difference between two stage least squares and instrumental variable regression?

I'm doing independent study and I am having trouble understanding the difference between these two estimators. I get that 2SLS is predicting the endogenous variable, and that instrumental variables ...
1 vote
1 answer
189 views

Testing for weak instrument

I have 3 endogenous variables in my model and I have identified 3 (or max 4) instruments. I wanted to know appropriate test for identifying whether the instruments are weak or not given that I have ...
0 votes
1 answer
36 views

Is it reasonable, in panel data, to use past values of explanatory variables as instruments to deal with simultaneous causality?

I am trying to examine the determinants of economic growth, essentially regressing a number of variables upon economic growth. I face a problem that there is likely simultaneous causality between many ...
5 votes
1 answer
9k views

Why are my 2SLS estimates much larger than my OLS estimates?

When performing IV regression, it is often taken as a sign of unbiasedness if the IV estimates are similar to the OLS estimates of the same model. My question is: If the estimates are very different,...
1 vote
0 answers
40 views

Weak Instrument - Stock and Yogo

I have the following structural equations where $G,Z$ are endogenous and $X,Y$ are exogenous $$ G_d=B_0+B_1Z+B_2X+u_1\\ G_s=a_0 +a_1Z+a_2Y+u_2 \\ G_d=G_s $$ Now, I would like to perform 2SLS, thus, ...
6 votes
2 answers
434 views

Instrumental Variable Paper for Minimum Wage

I am trying to write a paper dealing with minimum wages and employment. I understand there is simultaneity bias between these two variables so I must come up with an instrument. Does anyone have any ...
0 votes
0 answers
57 views

instrumental variables

I have a question related to IV methods. Suppose I have a regression $Y = a + b_1 X_1 + b_2 X_2 + \epsilon$, where $Y$ is a dependent variable and $X_1$ is an endogenous independent variable and $...
5 votes
1 answer
182 views

IV - Is this procedure valid?

I have three variables: $y$, $x_1$ and $z$. I'm interested in finding the effect of $x_1$ on $y$. Unfortunately $x_1$ is endogenous so I use an instrument z. I know that $z$ is correlated with $x_1$....
3 votes
1 answer
64 views

Imbens and Angrist (1994): the $D_i(z)$ variables

I'm referring to the Econometrica (1994) paper by Imbens and Angrist. In particular, I don't really understand the random variables $D_i(z)$ (defined on page 468). Could you please provide me with ...
2 votes
1 answer
75 views

Validity condition for Instrumental Variables

My professor states the validity condition in the following way: $W$ (the matrix of instrumental variables) must be such that $ \text{plim} \, \frac{W'u}{N}=0$, where $u$ is the error term. ...
5 votes
1 answer
2k views

Confounding versus endogenous variables. What is their relative hierarchical position?

There are valuable resources on the lexicon of types of variables quickly accessible, such as here. However, some of these concepts appear side-by-side often enough to make them confusing. For ...
1 vote
0 answers
39 views

Using an instrument in IV that is not strictly exogenous to the variable it is instrumenting?

I am considering instrumenting HIV with ODA, to evaluate the impact of HIV on gold mining. There is a clear relationship between HIV and ODA, however it may easily be argued this is an endogenous ...
2 votes
2 answers
568 views

Testing for Endogeneity

I apologize if this question is very basic. I have the following plain vanilla Instrumental Variable model. $Y=\alpha+X\beta+\varepsilon$ $X=\delta+Z\gamma+\eta$ $\varepsilon\perp\eta,\quad Z\perp\...